Exhibition hall with a pitched roof

An exhibition hall consists of a cuboid with a symmetric triangular-prism roof.

The hall is \(14\text{ m}\) long, \(9\text{ m}\) wide and has vertical walls \(4\text{ m}\) high. Each sloping roof edge in an end cross-section is \(6\text{ m}\).

The ridge is directly above the midpoint of the hall's width. Give non-exact numerical answers correct to \(3\) significant figures unless otherwise stated.

1. Show that the angle between a sloping roof edge and the horizontal is \(41.4^\circ\), correct to one decimal place.[2]
2. Find the volume of the hall.[3]
3. Find the vertical height of the ridge above the ground.[2]
4. From a bottom corner at one end, find the angle of elevation of the ridge point at the opposite end.[4]